Gravitational Clustering Algorithm Generalization by Using an Aggregation of Masses in Newton Law

The paper is devoted to the theoretical study of a specific clustering algorithm. Along the particular time steps of the algorithm the Newton gravitational law is used for attracting the particles each other. Our investigation is focused to a kind of generalization of Newton law by replacing the product of masses in the gravitational force equation by a more generalized aggregation of them. We study an overlap function employed, we establish a convergence criterion of such an algorithm. The controlling parameters that regulate the proximity of the particles and the convergence rate at the same time, are set up. The physical background of particle behaviour movement of which is governed by a generalized Newton gravitational force is provided along the investigation. The related geometrical interpretation is illustrated in figures.